Consider the two vectors A = Î - ĵ and B = - î - 2 j. (a) Calculate A + B î + -3 (b) Calculate A - B 2 When subtracting vectors that are given in component form, simply subtract the x components and then subtract the y components. ĵ v î + -1 (c) Calculate A + B 3 (d) Calculate A - B 1 The magnitude is determined from the Pythagorean theorem. (e) Calculate the directions of A + B and A - B. A + B A - B ° (counterclockwise from the +x axis) ° (counterclockwise from the +x axis)
Consider the two vectors A = Î - ĵ and B = - î - 2 j. (a) Calculate A + B î + -3 (b) Calculate A - B 2 When subtracting vectors that are given in component form, simply subtract the x components and then subtract the y components. ĵ v î + -1 (c) Calculate A + B 3 (d) Calculate A - B 1 The magnitude is determined from the Pythagorean theorem. (e) Calculate the directions of A + B and A - B. A + B A - B ° (counterclockwise from the +x axis) ° (counterclockwise from the +x axis)
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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![Consider the two vectors **A** = **î** – **ĵ** and **B** = – **î** – 2 **ĵ**.
**(a) Calculate \(\vec{A} + \vec{B}\)**
\[
\vec{A} + \vec{B} =
\begin{bmatrix}
0 \\
î \\
\end{bmatrix}
+
\begin{bmatrix}
-3 \\
j \\
\end{bmatrix}
\]
**Correct answer ✅**
**(b) Calculate \(\vec{A} - \vec{B}\)**
\[
\vec{A} - \vec{B} =
\begin{bmatrix}
2 \\
î \\
\end{bmatrix}
+
\begin{bmatrix}
-1 \\
j \\
\end{bmatrix}
\]
**Incorrect answer ❌**
Correction: When subtracting vectors that are given in component form, simply subtract the x components and then subtract the y components.
**(c) Calculate \(\Big| \vec{A} + \vec{B} \Big|\)**
\[
\Big| \vec{A} + \vec{B} \Big| = 3
\]
**Correct answer ✅**
**(d) Calculate \(\Big| \vec{A} - \vec{B} \Big|\)**
\[
\Big| \vec{A} - \vec{B} \Big| = 1
\]
**Incorrect answer ❌**
Correction: The magnitude is determined from the Pythagorean theorem.
**(e) Calculate the directions of \(\vec{A} + \vec{B}\) and \(\vec{A} - \vec{B}\)**
\[
\vec{A} + \vec{B} = \quad \boxed{}^\circ \, (counterclockwise\, from\, the \, +x\, axis)
\]
\[
\vec{A} - \vec{B} = \quad \boxed{}^\circ \, (counterclockwise\, from\, the \, +x\, axis)
\]
---
This transcription and explanation cover the essential calculations and corrections involved in vector addition, subtraction, and magnitude determination, important topics in advanced high school and university-level physics and mathematics.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbe5add6b-1715-412c-ae9e-e5ef4329e8a2%2Fa326b7c3-177c-435d-9234-3621c2170d5f%2Fpraj17v_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the two vectors **A** = **î** – **ĵ** and **B** = – **î** – 2 **ĵ**.
**(a) Calculate \(\vec{A} + \vec{B}\)**
\[
\vec{A} + \vec{B} =
\begin{bmatrix}
0 \\
î \\
\end{bmatrix}
+
\begin{bmatrix}
-3 \\
j \\
\end{bmatrix}
\]
**Correct answer ✅**
**(b) Calculate \(\vec{A} - \vec{B}\)**
\[
\vec{A} - \vec{B} =
\begin{bmatrix}
2 \\
î \\
\end{bmatrix}
+
\begin{bmatrix}
-1 \\
j \\
\end{bmatrix}
\]
**Incorrect answer ❌**
Correction: When subtracting vectors that are given in component form, simply subtract the x components and then subtract the y components.
**(c) Calculate \(\Big| \vec{A} + \vec{B} \Big|\)**
\[
\Big| \vec{A} + \vec{B} \Big| = 3
\]
**Correct answer ✅**
**(d) Calculate \(\Big| \vec{A} - \vec{B} \Big|\)**
\[
\Big| \vec{A} - \vec{B} \Big| = 1
\]
**Incorrect answer ❌**
Correction: The magnitude is determined from the Pythagorean theorem.
**(e) Calculate the directions of \(\vec{A} + \vec{B}\) and \(\vec{A} - \vec{B}\)**
\[
\vec{A} + \vec{B} = \quad \boxed{}^\circ \, (counterclockwise\, from\, the \, +x\, axis)
\]
\[
\vec{A} - \vec{B} = \quad \boxed{}^\circ \, (counterclockwise\, from\, the \, +x\, axis)
\]
---
This transcription and explanation cover the essential calculations and corrections involved in vector addition, subtraction, and magnitude determination, important topics in advanced high school and university-level physics and mathematics.
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